Question

Circumference of a circle or 2 times the perimeter of semi circle or 4 times the perimeter of a quarter circle? What can you say about their areas?

Answer 1

Area of circle , semi circle and quarter circle are same.

Step-by-step explanation:

Circumference of a circle  $= 2 \pi r$

Circumference (perimeter) of a semi circle  $= \pi r$

Given,

Circumference of a circle = 2 × Perimeter of semi circle

                                     $2 \pi r = 2 \times \pi r$

Hence, Both are same then their area will also same.

Now,

Circumference of a circle  $= 2 \pi r$

Perimeter of a quarter circle = $\frac{\pi r}{2}$

Given,

Circumference of a circle = 4 × Perimeter of quarter circle

                             $2 \pi r = 4 \times\frac{ \pi r}{2}$

                             $2 \pi r = 2 \pi r$

Hence,  Circumference of a circle and perimeter of quarter circle are same so their area will also same.